分层正方形格上的Rotor-Router聚集
Rotor-router aggregation on the layered square lattice
摘要：
在正方形格子Z ^2上的转子-路由器聚合中，从原点开始的粒子执行类似于随机游动的确定性行为，直到到达一个未被占据的位置。被占据的位点簇的极限形状是圆盘。我们考虑对x轴和y轴上的站点的路由机制进行小的更改，从而导致限制形状为菱形而不是圆盘。我们表明，对于一定的初始转子的选择，被占领的集群成长为一个完美的钻石。
英文摘要：
In rotor-router aggregation on the square lattice Z^2, particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site. The limiting shape of the cluster of occupied sites is a disk. We consider a small change to the routing mechanism for sites on the x- and y-axes, resulting in a limiting shape which is a diamond instead of a disk. We show that for a certain choice of initial rotors, the occupied cluster grows as a perfect diamond.
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